A local-global principle for rational isogenies of prime degree

作者：Sutherland Andrew V^*

来源：Journal de Theorie des Nombres de Bordeaux, 2012, 24(2): 475-485.

DOI：10.5802/jtnb.807

• elliptic curve
• isogeny
• local-global principle

Let K be a number field. We consider a local-global principle for elliptic curves E/K that admit (or do not admit) a rational isogeny of prime degree l. For suitable K (including K = Q), we prove that this principle holds for all l = 1 mod 4, and for l < 7, but find a counterexample when l = 7 for an elliptic curve with j-invariant 2268945/128. For K = Q we show that, up to isomorphism, this is the only counterexample.

• 出版日期2012